Question

In: Statistics and Probability

The given data set contains the amount of time(in minutes) students in an online course spent...

The given data set contains the amount of time(in minutes) students in an online course spent studying an assignment in a certain semester. According to the historical study, the mean time students would spend on this section nationwide is 95 minutes. While a researcher thinks that this semester student might be using more time. Use ? = 0.05 level of significance. Keep at least three decimal places for numerical answers.

(1) State the null hypothesis and alternative hypothesis for this researcher.

(2) Find the test statistic.

(3) Use critical value approach OR p-value approach to test the hypothesis. (If you use by-hand computation, show your steps; if you use Excel, provide the output)

(4) State the decision, then in the context of the research, state the conclusion.

Time (in minutes)
100
65
62
62
54
101
124
202
212
78
101
114
57
69
67
60
113
75
53
38
82
132
96
113
86
129
94
78
38
134
44
90
40
169
176
137
122
249
49
151
127
129
215
137
55
346

Solutions

Expert Solution

	Values ( X )
	100	85.361
	65	1957.098
	62	2231.5326
	62	2231.5326
	54	3051.3582
	101	67.8828
	124	217.8842
	202	8604.5846
	212	10559.8026
	78	975.8814
	101	67.8828
	114	22.6662
	57	2728.9236
	69	1619.1852
	67	1784.1416
	60	2424.489
	113	14.1444
	75	1172.316
	53	3162.8364
	38	5075.0094
	82	741.9686
	132	518.0586
	96	175.2738
	113	14.1444
	86	540.0558
	129	390.4932
	94	232.2302
	78	975.8814
	38	5075.0094
	134	613.1022
	44	4256.1402
	90	370.143
	40	4794.053
	169	3571.3652
	176	4457.0178
	137	770.6676
	122	162.8406
	249	19533.1092
	49	3628.7492
	151	1743.9728
	127	315.4496
	129	390.4932
	215	11185.368
	137	770.6676
	55	2941.88
	346	56055.7238
Total	5025	172278.371

Mean

Standard deviation

To Test :-

H0 :-

H1 :-

Test Statistic :-

t = 1.5608

Test Criteria :-
Reject null hypothesis if

Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 1.5608 ) = 0.0628
Reject null hypothesis if P value < level of significance
P - value = 0.0628 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that this semester student might be using more time at ? = 0.05 level of significance.

orchestra answered 1 year ago

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